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<p>The goal of this article is to construct high-order structure-preserving schemes for the coupled nonlinear fractional Klein–Gordon–Schrödinger equations. By carefully selecting two quadratic auxiliary variables, the original equations are reassembled to a new equivalent system, which inherits corresponding invariants including mass, modified quadratic energy and original Hamiltonian energy. Then Fourier pseudospectral method and symplectic Runge–Kutta methods are employed to discretize the space and time variables respectively. The proposed schemes can achieve spectral accuracy in spatial direction and arbitrarily high-order precision in temporal direction, and have remarkable capacity to maintain the mass and original energy in the discrete sense. By using matrix diagonalization approach and fast Fourier transform (FFT) algorithm, we also give an effective iterative method to solve the resulting nonlinear system. Finally, two numerical examples are performed to validate our theoretical analysis.</p>

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High-order energy-preserving methods for the coupled Klein–Gordon–Schrödinger equations with fractional Laplacian

  • 期刊论文

  • 发表日期：

    2025年5月19日

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  • Yulian Yi,
  • Mingfa Fei,
  • Hong Zhang,
  • Songhe Song

摘要

The goal of this article is to construct high-order structure-preserving schemes for the coupled nonlinear fractional Klein–Gordon–Schrödinger equations. By carefully selecting two quadratic auxiliary variables, the original equations are reassembled to a new equivalent system, which inherits corresponding invariants including mass, modified quadratic energy and original Hamiltonian energy. Then Fourier pseudospectral method and symplectic Runge–Kutta methods are employed to discretize the space and time variables respectively. The proposed schemes can achieve spectral accuracy in spatial direction and arbitrarily high-order precision in temporal direction, and have remarkable capacity to maintain the mass and original energy in the discrete sense. By using matrix diagonalization approach and fast Fourier transform (FFT) algorithm, we also give an effective iterative method to solve the resulting nonlinear system. Finally, two numerical examples are performed to validate our theoretical analysis.